Resistance of a Wire

Theory

What is resistance?

Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, i.e. it has less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions convert some of the energy that the free electrons are carrying into heat.

How is it measured?

The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula:

V = I Ò' R where V = Voltage, I = Current and R = Resistance

This can be rearranged to:

R = V

I

Ohm's Law

It is also relevant to know of Ohm's Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). Therefore V Ñ' I is constant. This means that the resistance of a metallic conductor is constant providing that the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons.

Variables

Input:

Length of wire. *

Material of wire.

Width of wire.

Starting temperature of wire.

Output:

and thus the resistance of the wire. †

Voltage across wire.

Current in circuit.

Temperature of wire.

The variable marked with a * will be varied, the other input variables will be kept constant. The output variable marked with a † will be measured.

Predictions

The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal. Therefore, more energy is going to be lost in these collisions (as heat).

Furthermore, doubling the length of the wire will result in double the resistance. This is because by doubling the length of the wire one is also doubling the collisions that will occur, thus doubling the amount of energy lost in these collisions.

Method

The following circuit was constructed to perform the investigation:

wire

The two dots ( ) represent the crocodile clips that were placed at the ends of the required length of wire.

1. One metre length of 0.4mm diameter "constantan" (a metal alloy) wire is fixed to a metre rule.

2. The first crocodile clip is clipped to the wire at the 0cm position on the metre rule.

3. The second crocodile clip is clipped to the relevant position depending on the required length of wire.

4. The power supply is turned on. The voltage and current are then read off the ammeter and voltmeter, and recorded.

5. The power supply is then turned off and the second crocodile clip is moved to the next position.